Ans the question no 34 .I have some doubt that how we can do this question without watching the answer. It is a question of some applications of trigonometry.

Let AB be the tower with A add top and B as bottom. Let C and D be the 2 station where BC equal to `a` and BD equal to `b` Construct a perpendicular AE in the direction it is bent such that EB equal to`x`ACB= alpha and ADB= betha and ABE = thetha.
Now you should be clear with diagram. We have to prove (cot thetha) =(b×cot alpha - a×cot betha)/(b-a). b cot alpha = {b(x + a)}/(AE). a cot betha = {a(b + x)}/(AE)
now (`b`cot alpha-`a`cot betha)/(b-a) = (bx+ab-ab-ax) / {AE(b-a)} =. x(b-a) / AE(b-a) = x /AE that is (cot thetha). Hence proved